On the Lagarias-Odlyzko algorithm for the subset sum problem
SIAM Journal on Computing
Probabilistic analysis of the multidimensional knapsack problem
Mathematics of Operations Research
Knapsack problems: algorithms and computer implementations
Knapsack problems: algorithms and computer implementations
Exponentially small bounds on the expected optimum of the partition and subset sum problems
Random Structures & Algorithms
Computing Partitions with Applications to the Knapsack Problem
Journal of the ACM (JACM)
Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
Random knapsack in expected polynomial time
Proceedings of the thirty-fifth annual ACM symposium on Theory of computing
On finding the exact solution of a zero-one knapsack problem
STOC '84 Proceedings of the sixteenth annual ACM symposium on Theory of computing
Computing equilibria for congestion games with (im)perfect information
SODA '04 Proceedings of the fifteenth annual ACM-SIAM symposium on Discrete algorithms
Typical properties of winners and losers in discrete optimization
STOC '04 Proceedings of the thirty-sixth annual ACM symposium on Theory of computing
Algorithm engineering: bridging the gap between algorithm theory and practice
Algorithm engineering: bridging the gap between algorithm theory and practice
Development of core to solve the multidimensional multiple-choice knapsack problem
Computers and Industrial Engineering
Connectedness and local search for bicriteria knapsack problems
EvoCOP'11 Proceedings of the 11th European conference on Evolutionary computation in combinatorial optimization
Smoothed analysis of integer programming
IPCO'05 Proceedings of the 11th international conference on Integer Programming and Combinatorial Optimization
Smoothed analysis of integer programming
IPCO'05 Proceedings of the 11th international conference on Integer Programming and Combinatorial Optimization
Efficient heuristic algorithms for path-based hardware/software partitioning
Mathematical and Computer Modelling: An International Journal
On local search for bi-objective knapsack problems
Evolutionary Computation
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We study the average-case performance of algorithms for the binary knapsack problem. Our focus lies on the analysis of so-called core algorithms, the predominant algorithmic concept used in practice. These algorithms start with the computation of an optimal fractional solution that has only one fractional item and then they exchange items until an optimal integral solution is found. The idea is that in many cases the optimal integral solution should be close to the fractional one such that only a few items need to be exchanged. Despite the well known hardness of the knapsack problem on worst-case instances, practical studies show that knapsack core algorithms can solve large scale instances very efficiently. For example, they exhibit almost linear running time on purely random inputs.In this paper, we present the first theoretical result on the running time of core algorithms that comes close to the results observed in practical experiments. We prove an upper bound of O(npolylog(n)) on the expected running time of a core algorithm on instances with n items whose profits and weights are drawn independently, uniformly at random. A previous analysis on the average-case complexity of the knapsack problem proves a running time of O(n4), but for a different kind of algorithms. The previously best known upper bound on the running time of core algorithms is polynomial as well. The degree of this polynomial, however, is at least a large three digit number. In addition to uniformly random instances, we investigate harder instances in which profits and weights are pairwise correlated. For this kind of instances, we can prove a tradeoff describing how the degree of correlation influences the running time.